You might be able to drive it over Ophir Pass, but even on that you will have to do multiple turns to get around the hairpins. I've had to do that on Ophir and Cinnamon Passes even with a mid-size truck (Ford Ranger and Nissan Frontier).
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Yeah, we have a long bed F350 4FWD and took it over Cinnamon. On a few hairpins I had to do some backing and froing to get around. It seems like those were mainly after the pass on the way down to the Animas ghost town. It was well worth it tho. The view from the pass is incredible, like nothing you'll see driving the paved roads in RMNP or Glacier. Engineer's pass road was closed on the west side so we missed that. I had been told the interconnect between Cinnamon and Engineers was not to be done in a big 4WD so we didn't try it.
When we stopped in Animas to look around some of the jeep drivers were asking us if we had any difficulty with the road. We really didn't, but we've driven a lot of 4WD roads of less vertical nature so we were mentally prepared. WE also hit some roads in Canyonlands that we just turned around on after hitting some 18 inch steps. And one terrifying road in Capitol Reef that made me a real believer in stopping when you hit a "JEEPS ONLY" sign. That one had me praying non-stop that we would live to the other end.
There were a lot of rental jeeps and quads going over Cinnamon. Think the jeeps were like $220/day in Ouray (where we we staying). One of those would be a better option for you.